reddit

“One can create an idealized mathematical model of a crystal by focusing on its main features, namely, the atoms and the bonds between them. The atoms are represented by points, which we will call "vertices", and the bonds are represented as lines, which we will call "edges". This kind of network of vertices and edges is called a "graph". A crystal is built up by starting with a building-block graph and joining together copies of itself in a periodic fashion. Thus there are two patterns operating in a crystal: The pattern of edges connecting vertices in the building-block graphs (that is, the pattern of bonding relations between the atoms), and the periodic pattern joining the copies of the graphs. One can create infinitely many mathematical crystals this way, by varying the graphs and by varying the way they are joined periodically.” source...